Home | | Maths 12th Std | Improper Integrals

Applications of Integration | Mathematics - Improper Integrals | 12th Maths : UNIT 9 : Applications of Integration

Chapter: 12th Maths : UNIT 9 : Applications of Integration

Improper Integrals

Applications of Integration: Improper Integrals

Improper Integrals

In defining the Riemann integral ab f ( x)dx , the interval [a , b] of integration is finite and f ( x) is finite at every point in [a , b] . In many physical applications, the following types of integrals arise:

a f ( x) dx , a− ∞ f ( x) dx , −∞ f ( x) dx ,


where a is a real number and f ( x) is a continuous function on the interval of integration. They are defined as the limits of Riemann integrals as follows:


They are called improper integrals of first kind. If the limits exist, then the improper integrals are said to be convergent.

Note

By the Fundamental theorem of integral calculus, there exists a function F (t) such that




Tags : Applications of Integration | Mathematics , 12th Maths : UNIT 9 : Applications of Integration
Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail
12th Maths : UNIT 9 : Applications of Integration : Improper Integrals | Applications of Integration | Mathematics

Related Topics

12th Maths : UNIT 9 : Applications of Integration


Privacy Policy, Terms and Conditions, DMCA Policy and Compliant

Copyright © 2018-2024 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.